Find the angle(s) of rotation that will carry a 12 sided polygon onto itself.

There are 2 ways of looking at this problem:

1. Mathematical
2. Logical

Personally, I think #2 is the most efficient way of answering:

When you think about it, in order to complete a full rotation, an object must rotate 360°. 

Therefore in order for a 12-sided polygon to rotate onto itself, the angle of rotation is 360°.

Hope this helps!